We study the freeness problem for matrix semigroups. We show that the freeness problem is decidable for upper-triangular 2 × 2 matrices with rational entries when the products are restricted to certain bounded languages. We also show that this problem becomes undecidable for sufficiently large matrices.

Abstract. Let Mn;m be the set of n-by-m matrices with entries inthe field of real numbers. A matrix R in Mn = Mn;n is a generalizedrow substochastic matrix (g-row substochastic, for short) if Re e, where e = (1; 1; : : : ; 1)t. For X; Y 2 Mn;m, X is said to besgut-majorized by Y (denoted by X sgut Y ) if there exists ann-by-n upper triangular g-row substochastic matrix R such thatX = RY . This ...

We consider a di erential inclusion system of the form _ x 2 Ax, where A is a collection of upper triangular matrices. Conditions for exponential stability of all the possible solutions are given.

Given a real, symmetric matrix S, we define the slice FS through S as being the connected component containing S of two orbits under conjugation: the first by the orthogonal group, and the second by the upper triangular group. We describe some classical constructions in eigenvalue computations and integrable systems which keep slices invariant — their properties are clarified by the concept. We...

The paper continues the study of recently introduced class SDD1 matrices. general matrices and its three subclasses are considered. In particular, it is shown that nonsingular ℌ-matrices. Also parameter-free upper bounds for l∞-norm inverses to derived. block triangular form which any matrix can be brought by a symmetric permutation rows columns described.

In this paper we prove that Neville elimination can be matricially described by elementary matrices. A PLU-factorization is obtained for any n×m matrix, where P is a permutation matrix, L is a lower triangular matrix (product of bidiagonal factors) and U is an upper triangular matrix. This result generalizes the Neville factorization usually applied to characterize the totally positive matrices...

; a ∈ A,m ∈ M, b ∈ B} equipped with the usual 2× 2 matrix-like addition and matrix-like multiplication is an algebra. An algebra T is called a triangular algebra if there exist algebras A and B and nonzero A−B-bimodule M such that T is (algebraically) isomorphic to Tri(A,M,B) under matrixlike addition and matrix-like multiplication; cf. [1]. For example, the algebra Tn of n × n upper triangular...

We describe an extension to ScaLAPACK for computing with symmetric (and hermitian) matrices stored in a packed form. This is similar to the compact storage for symmetric (and hermitian) matrices available in LAPACK [2]. This enables more efficient use of memory by storing only the lower or upper triangular part of a symmetric matrix. The capabilities include Choleksy factorization (PxSPTRF) and...

The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see R. Bacher. Determinants of matrices related to the Pascal triangle. J. Théor. Nombres Bordeaux, 14:19–41, 2002). This article presents a factorization by expressing such a matrix as a product of a unipotent lower triangular matrix, a Toeplitz matrix, and a unipotent upper triang...